Nonlinear vibration analysis of fiber metal laminated plates with multiple viscoelastic layers

To accurately predict the vibration behaviors of multiple viscoelastic-layered fiber metal laminated plates (MVFMLPs) under different external excitation levels, an analytical model accounting for both material and geometric nonlinearities is proposed in this paper. Firstly, by employing the Jones-Nelson nonlinear material theory together with the polynomial method and the energy-based strain energy principle, the nonlinear material properties of fiber and viscoelastic layers are expressed as functions of dimensionless strain energy density. Then, the equations of motion for MVFMLPs are derived considering the nonlinear strain–displacement relations of von Karman type. After the determination approach and procedure of the material fitting coefficients and Ritz parameters are clarified, vibration experiments on three MVFMLP specimens are undertaken to validate the developed model as well as evaluate the nonlinear vibration characteristics experimentally. Both theoretical and measured results indicate that the increase of base excitation amplitude not only leads to the ”perk swerve phenomenon” in the frequency-response curves of MVFMLPs, but also causes the complex changes in the natural frequencies and damping parameters due to the coupling influence of two types of nonlinear factors.